Zeroth-order (ZO) optimization offers a memory-efficient alternative to backpropagation for fine-tuning large language models. However, existing ZO methods typically sample training examples uniformly, overlooking their evolving importance and leaving avoidable estimation variance. To address this limitation, we propose Sample-Adaptive Zeroth-Order Optimization (SAZO), which learns sample importance online and adaptively allocates queries to accelerate convergence. SAZO extracts gradient-norm information from existing directional differences to estimate sample importance without access to true gradients. Furthermore, to track evolving importance from sparse minibatch feedback, SAZO maintains per-example exponential moving averages that aggregate observations across updates. The method requires no additional model evaluations and only O(N) additional scalar state compared with MeZO. We prove that SAZO asymptotically matches the leading convergence term of the minimum-variance sampling oracle, and achieves a strictly faster convergence rate than standard methods. Extensive experiments across four model families demonstrate improved average downstream performance and up to 6× faster convergence to the same training loss in terms of query count.
Zeroth-order optimization uses function values or comparisons, rather than gradients, to optimize objectives when differentiation is unavailable or costly.
Zeroth-Order optimization presents a promising memory-efficient paradigm for fine-tuning Large Language Models by relying solely on forward passes. However, its practical adoption is severely constrained by slow wall-clock convergence and high estimation variance. In this work, we dissect the runtime characteristics of ZO algorithms and identify a critical system bottleneck where the generation of perturbations and parameter updates accounts for over 40% of the training latency. We argue that the standard uniform exploration strategy is fundamentally flawed as it fails to account for the heterogeneous sensitivity of layers in deep networks, resulting in computationally wasteful blind searches. To address this structural mismatch, we propose AdaLeZO, an Adaptive Layer-wise ZO optimization framework. By formulating the layer selection process as a non-stationary Multi-Armed Bandit problem, AdaLeZO dynamically allocates the limited perturbation budget to the most sensitive parameters. We further introduce an Inverse Probability Weighting mechanism based on sampling with replacement, which guarantees unbiased gradient estimation while effectively acting as a temporal denoiser to reduce variance. Extensive experiments on LLaMA and OPT models ranging from 6.7B to 30B parameters demonstrate that AdaLeZO achieves 1.7x to 3.0x wall-clock acceleration compared to state-of-the-art methods. Crucially, AdaLeZO functions as a universal plug-and-play module that seamlessly enhances the efficiency of existing ZO optimizers without incurring additional memory overhead.
Fei Wang, Li Shen, Liang Ding +3
South China University of Technology · Shenzhen Campus of Sun Yat-sen University · University of Sydney +2
Zeroth-order (ZO) optimization with SGD in random subspaces enables memory-efficient fine-tuning of large language models without backpropagation. However, high gradient estimation noise fundamentally undermines adaptive optimizers like Adam. We propose SubZero+, which achieves practical adaptive ZO optimization through a carefully designed dual low-dimensionality strategy: (i) multi-query forward-difference gradient estimation in periodically refreshed random subspaces to mitigate noise amplification in moment buffers, and (ii) Adam updates with periodic restarts performed directly in low-dimensional space rather than full-parameter space. In experiments, this dual design retains memory overhead comparable to momentum-free ZO methods while achieving stronger optimization performance than the evaluated ZO baselines. Theoretically, in the exact-directional limit, K-query averaging preserves conditional unbiasedness, while the coefficient estimator's covariance and mean-squared error, as well as query-induced second-moment inflation, scale exactly as 1/K. Extensive experiments across SuperGLUE with models from 1.3B to 32B parameters under both full fine-tuning and LoRA schemes demonstrate consistent improvements over competing ZO methods. SubZero+ significantly narrows the performance gap with first-order optimization while preserving ZO's inference-time memory efficiency.
Ziming Yu, Shuyao Xiao, Xingyu Zhao +6
Beijing Normal University · Singapore Management University · Xiaomi Inc. +2
We investigate the effectiveness of adaptive zeroth-order (ZO) optimization for memory-constrained fine-tuning of large language models (LLMs). Contrary to prior claims, we show that adaptive ZO methods such as ZO-Adam offer no convergence advantage over well-tuned ZO-SGD, while incurring significant memory overhead. Our analysis reveals that in high dimensions, ZO gradients lack coordinate-wise heterogeneity, rendering adaptive mechanisms memory inefficient. Leveraging this insight, we propose MEAZO, a memory-efficient adaptive ZO optimizer that tracks only a single scalar for global step size adaptation. We support our method with theoretical convergence guarantees under standard assumptions. Experiments across multiple LLM families and tasks demonstrate that MEAZO matches ZO-Adam's performance with the memory footprint of ZO-SGD. Additional experiments on synthetic quadratic problems and LLM fine-tuning further demonstrate MEAZO's enhanced robustness to step size choices, particularly in grouped or block-structured optimization settings.